You are in the official 2003-2004 General Catalog
for California State University, Fresno.
Department of Mathematics
COURSES
- Mathematics (MATH)
- Mathematics (MATH) --- Graduate Courses
- Mathematics (MATH) --- In-Service Courses
Mathematics (MATH)
1RA. Developmental Mathematics I (3)
The first semester in a two semester sequence preparing students
for college level mathematics. Properties of ordinary arithmetic,
integers, rational numbers and linear equations. Enrollment restricted
to students scoring 30 or below on the Entry Level Math test.
CR/NC grading only; not applicable towards baccalaureate degree
requirements.
1RB. Developmental Mathematics II (3)
Prerequisite: MATH 1RA. The second semester in a two semester
sequence preparing students for college level mathematics. Systems
of linear equations, exponents, rational expressions, polynomials
and quadratic equations. CR/NC grading only; not applicable toward
baccalaureate degree requirements.
4R. Intermediate Algebra (3)
Prerequisite: ELM score 32 or above or permission of instructor.
Covers radicals, rational exponents, quadratic equations, simultaneous
linear equations, graphing, inequalities, and complex numbers.
CR/NC grading only; not applicable towards baccalaureate degree
requirements.
4RA. Intermediate Algebra (3)
Focuses on arithmetic review, linear equalities, inequalities,
and graphing. Note: MATH 4RA together with MATH 4RB is
equivalent to MATH 4R. Enrollment is limited to first-time freshmen
who score 30 and below on the ELM exam. CR/NC grading only; not
applicable towards baccalaureate degree requirements. (Formerly
MATH ILR)
4RB. Intermediate Algebra (3)
Prerequisite: MATH 4RA. Focuses on radicals, rational exponents,
and quadratic equations. Note: MATH 4RB together with MATH
4RA is equivalent to MATH 4R. Enrollment is limited to first-time
freshmen who score 30 and below on the ELM exam. CR/NC grading
only; not applicable towards baccalaureate degree requirements.
(Formerly MATH ILR)
4RL. Intermediate Algebra Laboratory (1)
Prerequisites: concurrently enrolled in MATH 4RA, 4RB, or MATH
4R and assigned to laboratory after taking placement examination.
Laboratory does not count toward baccalaureate degree. Extra review
and practice with skills essential to success in intermediate
algebra. CR/NC grading only; not applicable toward baccalaureate
degree requirements.
5. Trigonometry (3)
Prerequisite: students must meet the ELM requirement. Concept
of a function, sine and cosine functions, tables and graphs, other
trigonometric functions, identities and equations. Trigonometric
functions of angles, solution of triangles. (See Duplication of
Courses.) (CAN MATH 8)
6. Precalculus (4)
Prerequisite: students must meet the ELM requirement. Basic algebraic
properties of real numbers; linear and quadratic equations and
inequalities; functions and graphs; polynomials; exponential and
logarithmic functions; analytic trigonometry and functions; conics;
sequences, and series. (CAN MATH 16)
10A. Structure and Concepts in Mathematics I (3)
Prerequisite: students must meet the ELM requirement. No credit
for MATH 10A if taken after MATH 41. Designed for prospective
elementary school teachers. Development of real numbers including
integers, rational and irrational numbers, computation, prime
numbers and factorizations, and problem-solving strategies. Meets
B4 G.E. requirement only for liberal studies majors.
10B. Structure and Concepts in Mathematics II (3)
Prerequisite: MATH 10A or 41. Designed for prospective elementary
school teachers. Counting methods, elementary probability and
statistics. Topics in geometry to include polygons, congruence
and similarity, measurement, geometric transformations, coordinate
geometry, and connections between numbers and geometry with selected
applications.
11. Elementary Statistics (3)
Prerequisite: students must meet the ELM requirement. Illustration
of statistical concepts: elementary probability models, sampling,
descriptive measures, confidence intervals, testing hypotheses,
chi-square, nonparametric methods, regression. It is recommended
that students with credit in MATH 72 or 75 take MATH 101. (CAN
STAT 2)
14. Introduction to Discrete Mathematics (3)
No credit if taken after MATH 75. Prerequisite: students must
meet the ELM requirement. Set theory, relations and functions,
logic, proof techniques, number systems.
25. Mathematica (1)
Prerequisites: MATH 70, 71, 75 (may be taken concurrently) or
permission of instructor. In addition, students must meet the
ELM requirement. Use of Mathematica software as an exploratory
tool in Mathematics. Examples drawn from a broad range of Mathematics.
CR/NC grading only.
43. Elementary Problem Solving (3)
Prerequisite: students must meet the ELM requirement. The purpose
of this course is to develop problem-solving skills using elementary
mathematics.
45. What Is Mathematics? (3)
Prerequisite: students must meet the ELM requirement. Covers topics
from the following areas: (I) The Mathematics of Social Choice;
(II) Management Science and Optimization; (III) The Mathematics
of Growth and Symmetry; and (IV) Statistics and Probability. G.E.
Foundation B4.
61. Geometry and the Imagination (3)
Prerequisite: students must meet the ELM requirement. Topics in
Geometry. May include, but is not restricted to, tilings and tessellations,
regular polyhedra in 3 and 4 dimensions, ruler and compass constructions,
map coloring.
70. Mathematical Analysis for Life Sciences (4)
No credit if taken after MATH 72 or 75; one unit of credit if
taken after MATH 71. Prerequisite: students must meet the ELM
requirement. Functions and graphs, limits, derivatives, antiderivatives,
differential equations, and partial derivatives with applications
in the Life Sciences.
71. Elementary Mathematical Analysis I (3)
No credit if taken after MATH 70, 72, or 75. Prerequisite: students
must meet the ELM requirement. Review of algebra, real numbers,
inequalities, functions, graphs, finite induction, limits, differentiation
of algebraic functions and applications to extrema, mean value
theorem, l'Hôpital's rule.
72. Elementary Mathematical Analysis II (3)
No credit if taken after MATH 75; 2 units of credit if taken after
MATH 70. Prerequisites: MATH 71 and trigonometry. Analytic geometry
and calculus of polynomials, rational functions, transcendental
functions; polar coordinates, conic sections, integration and
applications.
75. Mathematical Analysis I (4)
Two units of credit if taken after MATH 70; 3 units of credit
if taken after MATH 71; 2 units of credit if taken after MATH
72. Prerequisite: elementary geometry, intermediate algebra, trigonometry,
or MATH 6. In addition, students must meet the ELM requirement.
Inequalities, functions, graphs, limits, continuity, derivatives,
antiderivatives, the definite integral, and applications. Using
Mathematica software as an exploratory tool. G.E. Foundation B4.
(CAN MATH 18)
76. Mathematical Analysis II (4)
Prerequisite: MATH 75. Transcendental functions, techniques of
integration, improper integrals, conic sections, polar coordinates,
infinite series. Using Mathematica software as an exploratory
tool. (CAN MATH 20)
77. Mathematical Analysis III (4)
Prerequisite: MATH 76. Vectors, three dimensional calculus, partial
derivatives, multiple integrals, Green's Theorem, Stokes' Theorem.
Using Mathematica software as an exploratory tool. (CAN MATH 22)
81. Applied Analysis (3)
Prerequisite: MATH 77. Introduction to ordinary linear differential
equations; solutions by power series and Laplace transforms. Solution
of systems of equations. Introduction to Fourier series. Using
Mathematica software as an exploratory tool.
90. Directed Study (1-3; max total 3)
Independently arranged course of study in some limited area of
mathematics either to remove a deficiency or to investigate a
topic in more depth. (1-3 hours, to be arranged)
100. Exploring Mathematics (3)
Prerequisite: MATH 10B. A problem-solving approach to topics from
game theory, combinatorics, mathematical modeling, and finite
geometries.
101. Statistical Methods (4)
Prerequisite: MATH 70, 71, or 75; no credit if taken after MATH
108. Application of statistical procedures to examples from biology,
engineering, and social science; one- and two-sample normal theory
methods; chi-square, analysis of variance, and regression; nonparametric
methods. Computerized statistical packages are used.
107. Introduction to Probability and Statistics (3)
Prerequisite: MATH 77 (may be taken concurrently). Basic concepts
required for applications of probability theory; standard discrete
and continuous models; random variables; conditional distributions;
limit theorems.
108. Statistics (3)
Prerequisite: MATH 107. Criteria used for selecting particular
procedures of data analysis; derivation of commonly used procedures;
topics from sampling, normal theory, nonparametrics, elementary
decision theory.
109. Applied Probability (3)
Prerequisite: MATH 107. Introduction to stochastic processes and
their applications in science and industry. Markov chains, queues,
stationary time series.
110. Symbolic Logic (3)
(Similar to PHIL 145; consult department.) Prerequisite: MATH
75. An informal treatment of the theory of logical inference,
statement calculus, truth-tables, predicate calculus, interpretations
applications.
114. Discrete Structures (3)
Prerequisite: MATH 76. Counting techniques, matrix algebra, graphs,
trees and networks, recurrence relations and generating functions,
applied modern algebra.
116. Theory of Numbers (4)
Prerequisite: MATH 75. Divisibility theory in the integers, primes
and their distribution, congruence theory, Diophantine equations,
number theoretic functions, primitive roots, indices, the quadratic
reciprocity law.
118. Graph Theory (3)
Prerequisite: MATH 77. Trees, connectivity, Euler and Hamilton
paths, matchings, chromatic problems, planar graphs, independence,
directed graphs, networks.
121. Numerical Analysis I (3)
Prerequisites: MATH 77 and CSCI 40. Zeros of nonlinear equations,
interpolation, quadrature, systems of equations, numerical ordinary
differential equations, and eigenvalues. Use of numerical software
libraries.
123. Topics in Applied Mathematics (3)
Prerequisite: MATH 77. Vector spaces and linear transformations,
eigenvalues and eigen functions. Special types of linear and nonlinear
differential equations; solution by series. Fourier transforms.
Special functions, including gamma, hypergeometric, Legendre,
Bessel, Laguerre, and Hermite functions. Introduction to partial
differential equations.
128. Applied Complex Analysis (3)
Prerequisite: MATH 77. Analytic functions of a complex variable,
contour integration, series, singularities of analytic functions,
the residue theorems, conformal mappings; emphasis on engineering
and physics applications.
133. Number Theory for Liberal Studies (3)
Prerequisite: MATH 10B or permission of instructor. The historical
development of the concept of number and arithmetic algorithms.
The magnitude of numbers. Basic number theory. Special numbers
and sequences. Number patterns. Modular arithmetic. (Formerly
NSCI 140T section)
134. Geometry for Liberal Studies (3)
Prerequisite: MATH 10B or permission of instructor. The use
of computer technology to study and explore concepts in Euclidean
geometry. Topics include, but are not restricted to, properties
of polygons, tilings, and polyhedra.
137. Exploring Statistics (3)
Prerequisite: MATH 10B or permission of instructor. Descriptive
and inferential statistics with a focus on applications to mathematics
education. Use of technology and activities for student discovery
and understanding of data organization, collection, analysis,
and inference.
138. Exploring Algebra (3)
Prerequisite: MATH 10B or permission of instructor. Designed for
prospective school teachers who wish to develop a deeper conceptual
understanding of algebraic themes and ideas needed to become competent
and effective mathematics teachers.
143. History of Mathematics (4)
Prerequisite: MATH 72 or 75. History of the development of mathematical
concepts in algebra, geometry, number theory, analytical geometry,
and calculus from ancient times through modern times. Theorems
with historical significance will be studied as they relate to
the development of modern mathematics.
145. Problem Solving (3)
Prerequisite: MATH 76. A study of formulation of problems into
mathematical form; analysis of methods of attack such as specialization,
generalization, analogy, induction, recursion, etc. applied to
a variety of non-routine problems. Topics will be handled through
student presentation.
151. Principles of Algebra (4)
Prerequisite: MATH 76. Equivalence relations; groups, cyclic groups,
normal subgroups, and factor groups; rings, ideals, and factor
rings; integral domains and polynomial rings; fields and field
extensions.
152. Linear Algebra (4)
Prerequisite: MATH 77. Vector spaces, linear transformations,
matrices, determinants, eigenvalues and eigenvectors, linear functions,
inner-product spaces, bilinear forms, quadratic forms, orthogonal
and unitary transformations, selected applications.
161. Principles of Geometry (3)
Prerequisite: MATH 77. The classical elliptic, parabolic, and
hyperbolic geometries developed on a framework of incidence, order
and separation, congruence; coordinatization. Theory of parallels
for parabolic and hyperbolic geometries. Selected topics of modern
Euclidean geometry.
165. Differential Geometry (3)
Prerequisite: MATH 77. Study of geometry in Euclidean space by
means of calculus, including theory of curves and surfaces, curvature,
theory of surfaces, and intrinsic geometry on a surface.
171. Intermediate Mathematical Analysis I (4)
Prerequisite: MATH 77. Sets, real numbers as a complete ordered
field, its usual topology, functions of a real variable, limits,
continuity, uniform continuity, differentiability, generalized
mean value theorem, Riemann integrals, series of functions, uniform
convergence, and Fourier series of integrable functions. (Formerly
MATH 171A)
172. Intermediate Mathematical Analysis II (4)
Prerequisite: MATH 171. Differentiation of functions of several
variables, applications of partial differentiation, functions
of bounded variation, rectifiable curves, theory of Riemann-Stieltjes
integration, multiple integrals and line integrals, improper Riemann-Stieltjes
integrals. Inverse and implicit function theorems.
181. Differential Equations (3)
Prerequisite: MATH 81 or 123. Definition and classification of
differential equations; general, particular, and singular solutions;
existence theorems; theory and technique of solving certain differential
equations: phase plane analysis, elementary stability theory;
applications.
182. Partial Differential Equations (3)
Prerequisites: MATH 81 or 123, and 171. Classical methods for
solving partial differential equations including separation of
variables, Green's functions, the Riemann-Volterra method and
Cauchy's problem for elliptic, parabolic, and hyperbolic equations;
applications to theoretical physics.
190. Independent Study (1-3; max total 6)
See Academic Placement -- Independent
Study. Approved for RP grading.
191T. Proseminar (1-3; max total 9)
Prerequisite: permission of instructor. Presentation of advanced
topics in mathematics in the field of the student's interest.
198. Senior Project (3)
Prerequisites: senior standing or permission of instructor; MATH
151, 171, and 152. Independent investigation and presentation
of an advanced topic in mathematics. Satisfies the senior major
requirement for the B.A. in Mathematics.
GRADUATE COURSES
(See Course Numbering System.)
Mathematics (MATH)
202. Fundamental Concepts of Mathematics (3)
Prerequisites: MATH 151, 161 and 171. Fundamental notions regarding
number theory, number systems, algebra of number fields; functions.
210. Foundations of Mathematics (3)
Prerequisite: MATH 110 or 151. Formal introduction to theories
of inference, first order theories, completeness metatheorems,
consistency metatheorems, decision problems.
216T. Topics in Number Theory (3; max total 6)
Prerequisite: MATH 116. An investigation of topics having either
historical or current research interest in the field of number
theory. (Formerly MATH 216)
221. Advanced Numerical Analysis (3)
Prerequisite: MATH 121. Linear equations and matrices; parabolic,
hyperbolic, and elliptic differential equations; constructive
function theory.
223. Principles and Techniques of Applied Mathematics (3)
Prerequisite: graduate standing or permission of instructor. Linear
spaces and spectral theory of operators.
224. Optimization Methods (3)
Prerequisite: graduate standing or permission of instructor. Techniques
for optimizing static and dynamic systems, calculus of variations,
Hamiltonian canonical form, maximum principle, with applications.
228. Functions of a Complex Variable (3)
Prerequisite: MATH 128. Representation theorems of Weierstrass
and Mittag-Leffler, normal families, conformal mapping and Riemann
mapping theorem, analytic continuation, Dirichlet problem.
232. Mathematical Models with Technology (3)
Prerequisite: graduate standing in mathematics or permission of
instructor. A technology-assisted study of the mathematics used
to model phenomena in statistics, natural science, and engineering.
250. Perspectives in Algebra (3)
Prerequisite: graduate standing in mathematics or permission of
instructor. Study of advanced topics in algebra, providing a higher
perspective to concepts in the high school curriculum. Topics
selected from, but not limited to, groups, rings, fields, and
vector spaces.
251. Abstract Algebra I (3)
Prerequisite: undergraduate abstract algebra. Groups, rings, integral
domains, and fields.
252. Abstract Algebra II (3)
Prerequisite: MATH 251. Rings and ideals, modules, linear and
multilinear algebras, representations.
260. Perspectives in Geometry (3)
Prerequisite: graduate standing in mathematics or permission of
instructor. Geometry from a transformations point of view. Euclidean
and noneuclidean geometries in two and three dimensions. Problem
solving and proofs using transformations. Topics chosen to be
relevant to geometrical concepts in the high school curriculum.
263. Point Set Topology (3)
Prerequisite: MATH 172. Basic concepts of point set topology,
set theory, topological spaces, continuous functions; connectivity,
compactness and separation properties of spaces. Topics selected
from function spaces, metrization, dimension theory.
265. Differential Geometry (3)
Prerequisites: MATH 165, 172. Study of geometry of curves and
surfaces in Euclidean space; including an introduction to Riemannian
geometry and theory of manifolds.
270. Perspectives in Analysis (3)
Prerequisite: graduate standing in mathematics or permission of
instructor. An overview of the development of mathematical analysis,
both real and complex. Emphasizes interrelation of the various
areas of study , the use of technology, and relevance to the high
school mathematics curriculum.
271. Real Variables (3)
Prerequisite: MATH 172. Theory of sets; cardinals; ordinals; function
spaces, linear spaces; measure theory; modern theory of integration
and differentiation.
272. Functional Analysis (3)
Prerequisite: MATH 271. The Lebesgue-Stieltjes integral and its
generalizations, integral equations, Hilbert and Banach spaces,
linear transformations (bounded and unbounded).
290. Independent Study (1-3; max total 6)
See Academic Placement -- Independent
Study. Approved for RP grading.
291. Seminar (3)
Prerequisite: graduate standing. Presentation of current mathematical
research in field of student's interest.
298. Research Project in Mathematics (3)
Prerequisite: graduate standing. Independent investigation of
advanced character as the culminating requirement for the master's
degree. Approved for RP grading.
IN-SERVICE COURSE
(See Course Numbering System.)
Mathematics (MATH)
302. Topics in Mathematics for Teachers (1-3; max
total 6 if topic not repeated)
Prerequisite: permission of instructor. Topics in modern mathematics
with special emphasis for teachers.
Mathematics
Degrees